Nonperturbative renormalization of Haldane pseudopotentials from the exact two-electron spectrum
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| Format: | Preprint |
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2026
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| author | Hai, G. -Q. Matsubara, M. T. Cândido, L. Brito, B. G. A. |
| author_facet | Hai, G. -Q. Matsubara, M. T. Cândido, L. Brito, B. G. A. |
| contents | Haldane pseudopotentials $V_{|m|}$ provide the effective interaction parameters governing correlated states in the fractional quantum Hall regime. In conventional formulations, these quantities are obtained by projecting the Coulomb interaction onto relative-angular-momentum states within the lowest Landau level, thereby neglecting virtual transitions to higher Landau levels. Here, we formulate a nonperturbative description of effective interactions directly from the exact two-electron spectrum in a magnetic field. By solving the relative-motion problem beyond the lowest-Landau-level approximation, we define renormalized pseudopotentials $V^*_{|m|}$ from the exact eigenenergies and introduce dynamical corrections $Δ_{|m|}=V^*_{|m|}-V_{|m|}$. The corrections remain systematically negative and depend strongly on both interaction strength and relative angular momentum, reflecting dynamical correlation effects associated with higher-state virtual admixture. The exact results reproduce the perturbative Landau-level-mixing limit at weak coupling while exhibiting substantial deviations in the strong-mixing regime, signaling the breakdown of low-order perturbative expansions. In particular, the short-range interaction channels relevant to Laughlin-type correlations undergo strong renormalization, leading to substantial modification of the effective interaction hierarchy in strongly interacting systems such as ZnO/MgZnO heterostructures. The present formulation establishes a microscopic framework for incorporating nonperturbative Landau-level-mixing effects into effective interaction theories of quantum Hall systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_31537 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonperturbative renormalization of Haldane pseudopotentials from the exact two-electron spectrum Hai, G. -Q. Matsubara, M. T. Cândido, L. Brito, B. G. A. Mesoscale and Nanoscale Physics Strongly Correlated Electrons Haldane pseudopotentials $V_{|m|}$ provide the effective interaction parameters governing correlated states in the fractional quantum Hall regime. In conventional formulations, these quantities are obtained by projecting the Coulomb interaction onto relative-angular-momentum states within the lowest Landau level, thereby neglecting virtual transitions to higher Landau levels. Here, we formulate a nonperturbative description of effective interactions directly from the exact two-electron spectrum in a magnetic field. By solving the relative-motion problem beyond the lowest-Landau-level approximation, we define renormalized pseudopotentials $V^*_{|m|}$ from the exact eigenenergies and introduce dynamical corrections $Δ_{|m|}=V^*_{|m|}-V_{|m|}$. The corrections remain systematically negative and depend strongly on both interaction strength and relative angular momentum, reflecting dynamical correlation effects associated with higher-state virtual admixture. The exact results reproduce the perturbative Landau-level-mixing limit at weak coupling while exhibiting substantial deviations in the strong-mixing regime, signaling the breakdown of low-order perturbative expansions. In particular, the short-range interaction channels relevant to Laughlin-type correlations undergo strong renormalization, leading to substantial modification of the effective interaction hierarchy in strongly interacting systems such as ZnO/MgZnO heterostructures. The present formulation establishes a microscopic framework for incorporating nonperturbative Landau-level-mixing effects into effective interaction theories of quantum Hall systems. |
| title | Nonperturbative renormalization of Haldane pseudopotentials from the exact two-electron spectrum |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.31537 |